The End Of Energy

Since the beginning of the Industrial Revolution, we have seen an
impressive and sustained growth in the scale of energy
consumption by human civilization. Plotting data from the Energy
Information Agency on U.S. energy use since 1650 (1635-1945,
1949-2009,
including wood, biomass, fossil fuels, hydro, nuclear, etc.)
shows a remarkably steady growth trajectory, characterized by an
annual growth rate of 2.9% (see figure). It is important to
understand the future trajectory of energy growth because
governments and organizations everywhere make assumptions based
on the expectation that the growth trend will continue as it has
for centuries—and a look at the figure suggests that this is a
perfectly reasonable assumption.

Growth has become such a mainstay of our existence that we take
its continuation as a given. Growth brings many positive
benefits, such as cars, television, air travel, and iGadgets.
Quality of life improves, health care improves, and, aside from a
proliferation of passwords to remember, life tends to become more
convenient over time. Growth also brings with it a promise of the
future, giving reason to invest in future development in
anticipation of a return on the investment. Growth is then the
basis for interest rates, loans, and the finance industry.

Because growth has been with us for “countless”
generations—meaning that everyone we ever met or our grandparents
ever met has experienced it—growth is central to our narrative of
who we are and what we do. We therefore have a difficult time
imagining a different trajectory.

This post provides a striking example of the impossibility of
continued growth at current rates—even within familiar
timescales. For a matter of convenience, we lower the energy
growth rate from 2.9% to 2.3% per year so that we see a factor of
ten increase every 100 years. We start the clock today, with a
global rate of energy use of 12 terawatts (meaning that the
average world citizen has a 2,000 W share of the total pie). We
will begin with semi-practical assessments, and then in stages
let our imaginations run wild—even then finding that we hit
limits sooner than we might think. I will admit from the start
that the assumptions underlying this analysis are deeply flawed.
But that becomes the whole point, in the end.

A Race to the Galaxy

I have always been impressed by the fact that as much solar
energy reaches Earth in one hour as we consume in a year. What
hope such a statement brings! But let’s not get carried away—yet.

Only 70% of the incident sunlight enters the Earth’s energy
budget—the rest immediately bounces off of clouds and atmosphere
and land without being absorbed. Also, being land creatures, we
might consider confining our solar panels to land, occupying 28%
of the total globe. Finally, we note that solar photovoltaics and
solar thermal plants tend to operate around 15% efficiency. Let’s
assume 20% for this calculation. The net effect is about 7,000
TW, about 600 times our current use. Lots of headroom, yes?

When would we run into this limit at a 2.3% growth rate? Recall
that we expand by a factor of ten every hundred years, so in 200
years, we operate at 100 times the current level, and we reach
7,000 TW in 275 years. 275 years may seem long on a single human
timescale, but it really is not that long for a civilization. And
think about the world we have just created: every square meter of
land is covered in photovoltaic panels! Where
do we grow food?

Now let’s start relaxing constraints. Surely in 275 years we will
be smart enough to exceed 20% efficiency for such an important
global resource. Let’s laugh in the face of thermodynamic limits
and talk of 100% efficiency (yes, we have started the fantasy
portion of this journey). This buys us a factor of five, or 70
years. But who needs the oceans? Let’s plaster them with 100%
efficient solar panels as well. Another 55 years. In 400 years,
we hit the solar wall at the Earth’s surface. This is
significant, because biomass, wind, and hydroelectric generation
derive from the sun’s radiation, and fossil fuels represent the
Earth’s battery charged by solar energy over millions of years.
Only nuclear, geothermal, and tidal processes do not come from
sunlight—the latter two of which are inconsequential for this
analysis, at a few terawatts apiece.

But the chief limitation in the preceding analysis is Earth’s
surface area—pleasant as it is. We only gain 16 years by
collecting the extra 30% of energy immediately bouncing away, so
the great expense of placing an Earth-encircling photovoltaic
array in space is surely not worth the effort. But why confine
ourselves to the Earth, once in space? Let’s think big: surround
the sun with solar panels. And while we’re at it, let’s again
make them 100% efficient. Never-mind the fact that a 4 mm-thick
structure surrounding the sun at the distance of Earth’s orbit
would require one Earth’s worth of materials—and specialized
materials at that. Doing so allows us to continue 2.3% annual
energy growth for 1350 years from the present time.

At this point you may realize that our sun is not the only star
in the galaxy. The Milky Way galaxy hosts about 100 billion
stars. Lots of energy just spewing into space, there for the
taking. Recall that each factor of ten takes us 100 years down
the road. One-hundred billion is eleven factors of ten, so 1100
additional years. Thus in about 2500 years from now, we would be
using a large galaxy’s worth of energy. We know in some detail
what humans were doing 2500 years ago. I think I can safely say
that I know what we won’t be doing 2500 years hence.

Why Single Out Solar?

Some readers may be bothered by the foregoing focus on
solar/stellar energy. If we’re dreaming big, let’s forget the
wimpy solar energy constraints and adopt fusion. The abundance of
deuterium in ordinary water would allow us to have a seemingly
inexhaustible source of energy right here on Earth. We won’t go
into a detailed analysis of this path, because we don’t have to.
The merciless growth illustrated above means that in 1400 years
from now, any source of energy we harness would have to
outshine the sun.

Let me restate that important point. No matter what the
technology, a sustained 2.3% energy growth rate would
require us to produce as much energy as the entire sun within
1400 years. A word of warning: that power plant is going to run a
little warm. Thermodynamics require that if we generated
sun-comparable power on Earth, the surface of the Earth—being
smaller than that of the sun—would have to be hotter
than the surface of the sun!

Thermodynamic Limits

We can explore more exactly the thermodynamic limits to the
problem. Earth absorbs abundant energy from the sun—far in excess
of our current societal enterprise. The Earth gets rid of its
energy by radiating into space, mostly at infrared wavelengths.
No other paths are available for heat disposal. The absorption
and emission are in near-perfect balance, in fact. If they were
not, Earth would slowly heat up or cool down. Indeed, we
have diminished the ability of infrared radiation to escape,
leading to global warming. Even so, we are still in balance to
within less than the 1% level. Because radiated power scales as
the fourth power of temperature (when expressed in absolute
terms, like Kelvin), we can compute the equilibrium temperature
of Earth’s surface given additional loading from societal
enterprise.

The result is shown above. From before, we know that if we
confine ourselves to the Earth’s surface, we exhaust solar
potential in 400 years. In order to continue energy growth beyond
this time, we would need to abandon renewables—virtually all of
which derive from the sun—for nuclear fission/fusion. But the
thermodynamic analysis says we’re toasted anyway.

Stop the Madness!

The purpose of this exploration is to point out the absurdity
that results from the assumption that we can continue growing our
use of energy—even if doing so more modestly than the last 350
years have seen. This analysis is an easy target for criticism,
given the tunnel-vision of its premise. I would enjoy shredding
it myself. Chiefly, continued energy growth will likely be
unnecessary if the human population stabilizes. At least the 2.9%
energy growth rate we have experienced should ease off as the
world saturates with people. But let’s not overlook the key
point: continued growth in energy use becomes physically
impossible within conceivable timeframes. The foregoing
analysis offers a cute way to demonstrate this point. I have
found it to be a compelling argument that snaps people into
appreciating the genuine limits to indefinite growth.

Once we appreciate that physical growth must one day cease (or
reverse), we can come to realize that all economic growth must
similarly end. This last point may be hard to swallow, given our
ability to innovate, improve efficiency, etc. But this topic will
be put off for another post.

Acknowledgments

I thank Kim Griest for comments and for seeding the idea that in
2500 years, we use up the Milky Way galaxy, and I thank Brian
Pierini for useful comments.